5. Transform each of the following LPs in standard form and identify the corresponding $A, c$ and $b$ in the matrix notation. (a) $$ \begin{array}{c) \min 4 x_{1}+2 x_{2}-33 x_{3} \text { s.t. }x_{1}-4 x_{2}+x_{3} \leq 12 W 9 x_{1}+6 x_{3}=15 W -5 x_{1}+9 x_{2} \geq 31 x_{1} \leq e, quad x_{3} \geq 0 \end{array $$ (b) $$ \begin{array}{c} \min -53 x_{1}+33\left(x_{2}+3 x_{3} ight) \text { s.t. }x_{j}+1 \leq x_{j+1} \quad \text { for } j=1,2 W \sum_{j=1}^{3}x_{j=10 \leq x_{j} \leq 3 \quad \text {for } j=1,2,3 \end{array} $$ SP.SD.479